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HIV infection is one of the most difficult infections to control and manage. The most recent recommendations to control this infection vary according to the guidelines used (US, European, WHO) and are not patient-specific. Unfortunately, no two individuals respond to infection and treatment quite the same way. The purpose of this paper is to make use of the uncertainty and sensitivity analysis to investigate possible short-term treatment options that are patient-specific. We are able to identify the most significant parameters that are responsible for ART outcome and to formulate some insights into the ART success. [ABSTRACT FROM AUTHOR]

Highly active antiretroviral therapy can effectively control HIV replication in infected individuals. Some clinical and modeling studies suggested that viral decay dynamics may depend on the inhibited stages of the viral replication cycle. In this paper, we develop a general mathematical model incorporating multiple infection stages and various drug classes that can interfere with specific stages of the viral life cycle. We derive the basic reproductive number and obtain the global stability results of steady states. Using several simple cases of the general model, we study the effect of various drug classes on the dynamics of HIV decay. When drugs are assumed to be 100 % effective, drugs acting later in the viral life cycle lead to a faster or more rapid decay in viremia. This is consistent with some patient and experimental data, and also agrees with previous modeling results. When drugs are not 100 % effective, the viral decay dynamics are more complicated. Without a second population of long-lived infected cells, the viral load decline can have two phases if drugs act at an intermediate stage of the viral replication cycle. The slopes of viral load decline depend on the drug effectiveness, the death rate of infected cells at different stages, and the transition rate of infected cells from one to the next stage. With a second population of long-lived infected cells, the viral load decline can have three distinct phases, consistent with the observation in patients receiving antiretroviral therapy containing the integrase inhibitor raltegravir. We also fit modeling prediction to patient data under efavirenz (a nonnucleoside reverse-transcriptase inhibitor) and raltegravir treatment. The first-phase viral load decline under raltegravir therapy is longer than that under efavirenz, resulting in a lower viral load at initiation of the second-phase decline in patients taking raltegravir. This explains why patients taking a raltegravir-based therapy were faster to achieve viral suppression than those taking an efavirenz-based therapy. Taken together, this work provides a quantitative and systematic comparison of the effect of different drug classes on HIV decay dynamics and can explain the viral load decline in HIV patients treated with raltegravir-containing regimens. [ABSTRACT FROM AUTHOR]

While antiretroviral drugs can drive HIV to undetectably low levels in the blood, eradication is hindered by the persistence of long-lived, latently infected memory CD4 T cells. Immune activation therapy aims to eliminate this latent reservoir by reactivating these memory cells, exposing them to removal by the immune system and the cytotoxic effects of active infection. In this paper, we develop a mathematical model that investigates the use of immune activation strategies while limiting virus and latent class rebound. Our model considers infection of two memory classes, central and transitional CD4 T cells and the role that general immune activation therapy has on their elimination. Further, we incorporate ways to control viral rebound by blocking activated cell proliferation through anti proliferation therapy. Using the model, we provide insight into the control of latent infection and subsequently into the long term control of HIV infection. [ABSTRACT FROM AUTHOR]

simple mathematical model (Granich et al., Lancet 373:48-57, ) suggested recently that annual HIV testing of the population, with all detected HIV individuals immediately treated with antiretrovirals, could lead to the long-term decline of HIV in South Africa and could save millions of lives in the next few years. However, the model suggested that the long-term decline of HIV could not be achieved with less frequent HIV testing. Many observers argued that an annual testing rate was very difficult in practice. Small scale trials are nevertheless in preparation. In this paper, we use a more realistic age-structured model, which suggests that the recent high levels of reported condom use could already lead to a long-term decline of HIV in South Africa. The model therefore suggests that trials with for example 20% of the population tested each year would also be interesting. They would have similar (though smaller) advantages in terms of reduction of mortality and incidence, would be much easier to generalize to larger populations, and would not lead to long term persistence of HIV. Our model simulations also suggest that the age distribution of incidence has changed considerably over the past 20 years in South Africa. This raises some concern about an assumption presently used in EPP/Spectrum, the software used by UNAIDS for its estimates. [ABSTRACT FROM AUTHOR]

A recent randomized controlled trial shows a significant reduction in women-to-men transmission of HIV due to male circumcision. Such development calls for a rigorous mathematical study to ascertain the full impact of male circumcision in reducing HIV burden, especially in resource-poor nations where access to anti-retroviral drugs is limited. First of all, this paper presents a compartmental model for the transmission dynamics of HIV in a community where male circumcision is practiced. In addition to having a disease-free equilibrium, which is locally-asymptotically stable whenever a certain epidemiological threshold is less than unity, the model exhibits the phenomenon of backward bifurcation, where the disease-free equilibrium coexists with a stable endemic equilibrium when the threshold is less than unity. The implication of this result is that HIV may persist in the population even when the reproduction threshold is less than unity. Using partial data from South Africa, the study shows that male circumcision at 60% efficacy level can prevent up to 220,000 cases and 8,200 deaths in the country within a year. Further, it is shown that male circumcision can significantly reduce, but not eliminate, HIV burden in a community. However, disease elimination is feasible if male circumcision is combined with other interventions such as ARVs and condom use. It is shown that the combined use of male circumcision and ARVs is more effective in reducing disease burden than the combined use of male circumcision and condoms for a moderate condom compliance rate. [ABSTRACT FROM AUTHOR]

The discrepancy in the turnover of cells and virus in different organs or viral reservoirs necessitates the investigation of multiple compartments within a host. Establishing a multi-compartmental structure that describes the complexity of various organs, where viral infection comprehensively proceeds, provides a modeling framework for exploring the effect of spatial heterogeneity on viral dynamics. To successfully suppress within-host viral replication, it is imperative to determine drug administration during therapy, particularly for a combination of antiretroviral drugs. The proposed model provides quantitative insights into pharmacokinetics and the resulting virus population, which substantially relates to environmental heterogeneity. The main results are the following: (1) A model incorporating drug treatment admits threshold dynamics, driving to either viral extinction or uniform persistence, regardless of non-trivial initial infection, in the entire system. (2) Viral infection may be underestimated if a well-mixed (single-compartmental) model is used. (3) Optimal drug administration depends not only on the drug distribution over various compartments but also on the timing, described by phase shifts, of the administration of different drugs in a combined therapy. [ABSTRACT FROM AUTHOR]

The presence of cells latently infected with HIV is currently considered to be a major barrier to viral eradication within a patient. Here, we consider birth-death-immigration models for the latent cell population in a single patient, and present analytical results for the size of this population in the absence of treatment. We provide results both at steady state (viral set point), and during the non-equilibrium setting of early infection. We obtain semi-analytic results showing how latency-reversing drugs might be expected to affect the size of the latent pool over time. We also analyze the probability of rare mutant viral strains joining the latent cell population, allowing for steady-state and dynamic viral populations within the host. [ABSTRACT FROM AUTHOR]

Immune interventions consisting in repeated injections are broadly used as they are thought to improve the quantity and the quality of the immune response. However, they also raise several questions that remain unanswered, in particular the number of injections to make or the delay to respect between different injections to achieve this goal. Practical and financial considerations add constraints to these questions, especially in the framework of human studies. We specifically focus here on the use of interleukin-7 (IL-7) injections in HIV-infected patients under antiretroviral treatment, but still unable to restore normal levels of CD4+ T lymphocytes. Clinical trials have already shown that repeated cycles of injections of IL-7 could help maintaining CD4+ T lymphocytes levels over the limit of 500 cells/μL, by affecting proliferation and survival of CD4+ T cells. We then aim at answering the question: how to maintain a patients level of CD4+ T lymphocytes by using a minimum number of injections (i.e., optimizing the strategy of injections)? Based on mechanistic models that were previously developed for the dynamics of CD4+ T lymphocytes in this context, we model the process by a piecewise deterministic Markov model. We then address the question by using some recently established theory on impulse control problem in order to develop a numerical tool determining the optimal strategy. Results are obtained on a reduced model, as a proof of concept: the method allows to define an optimal strategy for a given patient. This method could be applied to optimize injections schedules in clinical trials. [ABSTRACT FROM AUTHOR]